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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
184 lines
6.7 KiB
Markdown
184 lines
6.7 KiB
Markdown
# VO: Volume Oscillator
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> *Volume tells us the conviction behind price moves—the oscillator reveals when that conviction is accelerating or fading.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Volume |
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| **Inputs** | OHLCV bar (TBar) |
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| **Parameters** | `shortPeriod` (default 5), `longPeriod` (default 10), `signalPeriod` (default 10) |
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| **Outputs** | Single series (Vo) |
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| **Output range** | Unbounded |
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| **Warmup** | 1 bar |
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| **PineScript** | [vo.pine](vo.pine) |
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- The Volume Oscillator (VO) measures the difference between two moving averages of volume, expressed as a percentage.
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- **Similar:** [PVO](../pvo/Pvo.md), [VROC](../vroc/Vroc.md) | **Complementary:** Price confirmation | **Trading note:** Volume Oscillator; difference of two volume MAs. Confirms price moves with volume expansion.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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The Volume Oscillator (VO) measures the difference between two moving averages of volume, expressed as a percentage. It helps identify changes in volume trends and potential momentum shifts by comparing short-term volume activity against longer-term volume norms.
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## Historical Context
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Volume analysis has been a cornerstone of technical analysis since the early 20th century. Charles Dow emphasized volume as a key confirmation tool for price movements. The Volume Oscillator emerged as traders sought a normalized way to compare volume across different timeframes, similar to how price oscillators like MACD compare price moving averages.
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The indicator gained popularity because raw volume numbers vary dramatically across securities and time periods. By expressing the difference between volume averages as a percentage, VO provides a consistent scale for comparison regardless of the underlying security's typical trading volume.
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## Architecture & Physics
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### 1. Short-Term Volume SMA
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The short-term simple moving average captures recent volume activity:
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$$
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\text{ShortMA}_t = \frac{1}{n_s} \sum_{i=0}^{n_s-1} V_{t-i}
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$$
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where $n_s$ is the short period (default: 5) and $V$ is volume.
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### 2. Long-Term Volume SMA
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The long-term simple moving average establishes the volume baseline:
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$$
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\text{LongMA}_t = \frac{1}{n_l} \sum_{i=0}^{n_l-1} V_{t-i}
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$$
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where $n_l$ is the long period (default: 10).
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### 3. Volume Oscillator Calculation
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The oscillator expresses the difference as a percentage:
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$$
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\text{VO}_t = \frac{\text{ShortMA}_t - \text{LongMA}_t}{\text{LongMA}_t} \times 100
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$$
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This normalization allows:
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- Positive values when short-term volume exceeds long-term average
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- Negative values when short-term volume is below long-term average
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- Comparable readings across different securities
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### 4. Signal Line
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An optional signal line smooths the VO for trend identification:
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$$
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\text{Signal}_t = \frac{1}{n_{sig}} \sum_{i=0}^{n_{sig}-1} \text{VO}_{t-i}
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$$
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where $n_{sig}$ is the signal period (default: 10).
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## Mathematical Foundation
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### Running Sum Implementation
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For O(1) updates, we maintain running sums rather than recalculating:
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$$
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\text{Sum}_t = \text{Sum}_{t-1} - V_{t-n} + V_t
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$$
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where $V_{t-n}$ is the oldest value being removed from the window.
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### Division Safety
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To prevent division by zero:
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$$
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\text{VO}_t = \begin{cases}
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\frac{\text{ShortMA}_t - \text{LongMA}_t}{\text{LongMA}_t} \times 100 & \text{if } \text{LongMA}_t > 0 \\
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0 & \text{otherwise}
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\end{cases}
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$$
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### Period Constraint
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The short period must be strictly less than the long period:
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$$
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n_s < n_l
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$$
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This ensures the indicator measures the relationship between recent and historical volume, not vice versa.
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## Performance Profile
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### Operation Count (Streaming Mode, Scalar)
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| ADD/SUB | 6 | 1 | 6 |
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| MUL | 1 | 3 | 3 |
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| DIV | 3 | 15 | 45 |
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| CMP/MOD | 6 | 1 | 6 |
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| **Total** | **16** | — | **~60 cycles** |
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The running sum approach eliminates the need to iterate over the entire window each update.
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### Memory Footprint
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Per instance:
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- Short buffer: $n_s \times 8$ bytes
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- Long buffer: $n_l \times 8$ bytes
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- Signal buffer: $n_{sig} \times 8$ bytes
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- State: ~128 bytes
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With defaults (5, 10, 10): ~328 bytes per instance.
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 9/10 | Exact SMA calculation |
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| **Timeliness** | 7/10 | Inherent SMA lag |
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| **Overshoot** | 8/10 | Bounded by percentage scale |
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| **Smoothness** | 7/10 | Depends on periods chosen |
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## Interpretation
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### Signal Reading
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| VO Value | Interpretation |
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| :--- | :--- |
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| **> 0** | Short-term volume above average (accumulation/distribution) |
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| **< 0** | Short-term volume below average (consolidation) |
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| **Rising** | Volume momentum increasing |
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| **Falling** | Volume momentum decreasing |
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### Trading Applications
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1. **Trend Confirmation**: Rising VO during price uptrends confirms bullish momentum
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2. **Divergence**: Price making new highs while VO declining suggests weakening trend
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3. **Signal Crossovers**: VO crossing above signal line suggests volume momentum shift
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4. **Zero-Line Crossings**: VO crossing above zero indicates short-term volume exceeding long-term average
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## Validation
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| Library | Status | Notes |
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| :--- | :---: | :--- |
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| **TA-Lib** | N/A | Not implemented |
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| **Skender** | N/A | Not implemented |
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| **Tulip** | N/A | Not implemented |
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| **Ooples** | N/A | Not implemented |
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| **PineScript** | ✅ | Reference implementation |
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## Common Pitfalls
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1. **Period Selection**: Short period too close to long period produces noisy signals. Recommend at least 2:1 ratio (e.g., 5 and 10, or 12 and 26).
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2. **Zero Volume Handling**: Securities with occasional zero volume bars can distort calculations. Implementation uses minimum volume of 1.0 to avoid division issues.
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3. **Warmup Period**: Full accuracy requires at least `longPeriod` bars. Before warmup, results use partial window averages.
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4. **Percentage Interpretation**: VO of +20% means short-term volume is 20% above long-term average, not that volume increased by 20%.
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5. **Signal Line Lag**: The signal line adds additional smoothing delay. For faster signals, reduce signal period or use VO directly.
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6. **Bar Correction**: When using `isNew=false`, all three SMA buffers must be restored for accurate recalculation.
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## References
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- Murphy, J. J. (1999). *Technical Analysis of the Financial Markets*. New York Institute of Finance.
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- Achelis, S. B. (2001). *Technical Analysis from A to Z*. McGraw-Hill.
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- PineScript Reference: vo.pine |